Question

In Star wars Princess Leia and Han Solo happen to leave the Death Star . They are
escaping in X wing at a speed of 200m/s. They happen to be spotted by clones who
launch a missile at them. Leia calculates that the speed of the missile is 300m/s. PrincessLeia calculates that the missile is 3km away. She asks Han Solo to accelerate to 350m/s. The maximum acceleration of the X wing fighter craft is surprisingly 25m/s2 Find the time taken by X wing to reach the speed of 350m/s. Noe the missile is launched from the samelaunchpad as their Xwing fighter craft, so everything is in straight line.

Answer 1

Answer:

6 seconds

Explanation:

It is given that:

Initial Speed of X wing, u = 200 m/s

Speed to be attained = 350 m/s

i.e. Final speed, v = 350 m/s

Maximum acceleration of X wing = 25 m/s

a = 25 m/s

To find, the time taken to reach the speed of 350 m/s

Given that:

$u = 200\ m/s\\v = 350\ m/s\\a = 25\ m/s^2$

$t=?$

We know the formula:

$v=u+at$

Putting the values of $u, v, a$ and trying to find $t$:

$350 = 200 +25\times t\\\Rightarrow 25t =350-200\\\Rightarrow 25t =150\\\Rightarrow t = \dfrac{150}{25}\\\Rightarrow t =6\ s$

So, Time taken to reach to a speed of 350 m/s is 6 seconds.

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Speed of missile is = 300 m/s

Distance traveled by missile in 6 seconds = 300 $\times$ 6 = 1800 m = 1.8 km

And distance between missile and X wing is 3 kms.

So, X wing will be able to reach to a speed (350 m/s) greater than that of missile (300 m/s) before the missile could reach the X wing.

Hence, X wing will be safe.

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So, Time taken to reach to a speed of 350 m/s is 6 seconds.